Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774000 | Journal of Differential Equations | 2017 | 16 Pages |
Abstract
In this paper, we prove some Liouville theorem for the following elliptic equations involving nonlocal nonlinearity and nonlocal boundary value condition{âÎu(y)=â«âR+NF(u(xâ²,0))|(xâ²,0)ây|Nâαdxâ²g(u(y)),yâR+N,âuâν(xâ²,0)=â«R+NG(u(y))|(xâ²,0)ây|Nâαdyf(u(xâ²,0)),(xâ²,0)ââR+N, where R+N={xâRN:xN>0}, f,g,F,G are some nonlinear functions. Under some assumptions on the nonlinear functions f,g,F,G, we will show that this equation doesn't possess nontrivial positive solution. We extend the Liouville theorems from local problems to nonlocal problem. We use the moving plane method to prove our result.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xiaohui Yu,